Perimeter and Area of Plane Figures
80. Area of a Rectangle · length times breadth
The area is always length times breadth.
Area of a rectangle = length × breadth. If a rectangle has length l and breadth b, its area is A = l × b (in square units). Drag the corner — area updates as the dimensions change.
What this lesson covers
Try to break it
Watch how the area changes as you resize the rectangle.
How you build it
Construct a rectangle.
- Place point A, the first corner of the rectangle.
- Place point B. The segment AB will be the length of the rectangle.
- Draw the segment from A to B.
- Construct a line through A, perpendicular to AB — this carries the breadth.
- Construct a line through B, perpendicular to AB — the opposite breadth runs along it.
- Mark point D on the perpendicular through A, above AB. The segment AD is the breadth of the rectangle.
- Set the compass opening to AD — click A, then D. This locks the compass to the breadth.
- With the compass still set to AD, draw an arc centred at B — click B. It crosses the perpendicular at B.
- Mark point C where the arc crosses the perpendicular at B — the fourth corner.
- Draw the segment from D to C. Opposite sides are equal and all four angles are right angles — ABCD is a rectangle.
The proof, step by step
Prove that the area of a rectangle equals length × breadth.
- Imagine covering the rectangle completely with 1×1 unit squares.
- Each horizontal row contains exactly 'l' squares.
- There are exactly 'b' such rows stacked vertically.
- Total squares = l × b, so Area = length × breadth.
Worked example
A rectangular garden has a length of 15 meters and a breadth of 8 meters. Find the area of the garden.
Area = length × breadth = 15 × 8 = 120 m².
- 120 m² — correct
- 23 m²
- 46 m²
- 120 m